Hi Anup,

On motivation...

I think a lot of difficult high-level vision problems can be cast as finding a manifold that's embedded in some higher-dimensional search space. An example in the paper is face recognition in variable lighting. Here the approach was to cast the face as a lambertian surface, then use clustering to partition the dataset into same-surface objects. The goal here is the same as in the Sivic paper you presented -- unsupervised class discovery. The classes in this case are the individuals (same surface = same face).

You could imagine other examples. Region tracking with optical flow is one. The search space is 4D -- location and velocity for each pixel. The regions might be curves or surfaces in this search space. How can you extract these regions? The k-lines problem is essentially doing exactly this. If there were just one region, RANSAC might work well. But if there are several regions, you'd need a method such as this one.